Question

encode the word SECRET using the Matrix concept​

Answer 1

Answer:

Let the word in numbers be M=19, 5, 3, 18, 5, 20

Step-by-step explanation:

In the matrix M, A=1, B=2, C=3 and so on.

Thus the word SECRET will be M.

Now, lets split M into 2 matrices of 3x3 size each Namely A and B.

A =   $\left[\begin{array}{ccc}19\\5\\3\end{array}\right]$ and B= $\left[\begin{array}{ccc}18\\5\\20\end{array}\right]$.

Now we need to decide on a coding matrix.

Let's take X= $\left[\begin{array}{ccc}1&2&3\\0&1&4\\7&8&9\end{array}\right]$

         

Now, A.X=  $\left[\begin{array}{ccc}1&2&3\\0&1&4\\7&8&9\end{array}\right]$ $\left[\begin{array}{ccc}19\\5\\3\end{array}\right]$

               = $\left[\begin{array}{ccc}38\\17\\200\end{array}\right]$

And, B.X=  $\left[\begin{array}{ccc}1&2&3\\0&1&4\\7&8&9\end{array}\right]$ $\left[\begin{array}{ccc}18\\5\\20\end{array}\right]$

             =   $\left[\begin{array}{ccc}88\\85\\346\end{array}\right]$

The Encoded message is 38, 119, 200, 88, 217, 346.

All you need to decode it is to find A⁻¹.

which will be A⁻¹ = $\left[\begin{array}{ccc}-23/12&1/2&5/12\\7/3&-1&-1/3\\-7/12&1/2&1/12\end{array}\right]$

When you multiply this matrix with A.X and B.X you will get back the original matrix of M= 19,5,3,18,5,20.

Hope this helps.

Answer 2

Answer

102, 73, 102, 63, 120, 75

Step1 : Letter to numbers

Used A=1,B=2.........

SECRET = 19, 5, 3, 18, 5, 20

When the letters are changed to numbers, my message reads as:

19, 5, 3, 18, 5, 20

But remember, we are doing this with matrixes and letters in groups of two, so it will be

[19 5] [3 18] [5 20]

Step 2 : The Key

The key matrix is (2x2 matrix)

[4 3]

[5 3]

Let key matrix be [K]

Step 3 : Multiply

[19 5]x[K] = [102 72]

[3 18]x[K]= [102 63]

[5 20]x[K] = [120 75]

Step 4: Rewrite

From step 3 we get the sequence as

102, 73, 102, 63, 120, 75